Boxer with brio occasionally providing cover story (5)
I believe the answer is:
alibi
'cover story' is the definition.
'boxer with brio occasionally' is the wordplay.
'boxer' becomes 'ali' (Muhammad Ali).
'with' says to put letters next to each other.
'occasionally' indicates alternate letters.
The alternate letters of 'brio' are 'bi'.
'ali'+'bi'='ALIBI'
'providing' acts as a link.
(Other definitions for alibi that I've seen before include "can offer a valid defence against most charges" , "Answer to charge - was somewhere else" , "Timely excuse" , "Defence used by an accused person" , "it may help you to get off" .)